How to write a number in standard form

Would you like to learn how to write huge or very small numbers in simple form? This article contains the necessary explanations and very clear rules on how to do this. Theoretical material will help to understand this rather easy topic.

Very high values

Suppose there is a certain number. Could you quickly say how it is read, or how great is its significance?

100000000000000000000

Nonsense, right? Few people can cope with such a task. Even if there is a specific name for such a value, in practice it may not be remembered. This is why it is customary to use the standard view instead. It is much simpler and faster.

Standard view

The term can mean many different things, depending on which area of ​​mathematics we are dealing with. In our case, this is another name for the scientific record of numbers.

She is really simple. It looks as follows:

ax 10 ⁿ

In these notations:

a is a number called a coefficient.

The coefficient must be greater than or equal to 1, but less than 10.

“X” is the sign of multiplication;

10 is the basis;

n is an indicator, a power of tens.

Thus, the resulting expression reads as "a ten to the nth power."

Take a concrete example for a complete understanding:

2 x 10 ³

Multiplying the number 2 by 10 in the third power, we get 2000 as a result. That is, we have a couple of equivalent variants of writing the same expression.

Conversion algorithm

Take some number.

300000000000000000000000000000

In calculations, using such a number is inconvenient. Let's try to bring it to its standard form.

1. Count the number of zeros on the right side of the triple. Get twenty nine.
2. We drop them, leaving only a single digit. It is equal to three.
3. Add to the result the multiplication sign and ten to the power found in paragraph 1.

3 x 10 ²⁹ .

So easy to get an answer.

If there were still others before the first non-zero digit, the algorithm would have changed slightly. I would have to perform the same actions, however, the value of the indicator would be calculated by zeros on the left and would have a negative value.

0.0003 = 3 x 10 ^-4

Converting a number facilitates and accelerates mathematical calculations, makes the solution record more compact and intuitive.